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Question

# A man running on horizontal road finds the rain falling at angle α with the vertical. If he doubles his speed angle becomes β. With what angle with vertical whill rain appear to fall, when he triples his speed? The rain falls vertically down when he is at rest.

A
tan1(2 tanαtanβ)
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B
tan1(2 tanβ+tanα)
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C
tan1(2 tanα+tanβ)
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D
tan1(2 tanβtanα)
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Solution

## The correct option is D tan−1(2 tanβ−tanα)Let the initial speed of the man be V. −−→VMO=V^i Let −−→VRO=−x^j(constant) tanα=VMOVRO=Vx when he doubles his speed. tanβ=2Vx when he triples his speed, tanγ=3Vx 2tanβ−tanα=4Vx−Vx=3Vx ⇒2tanβ−tanα=tanγ ⇒γ=tan−1(2tanβ−tanα)

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